Download Macroeconomic Effects Of Quantitative Easing

GHENT UNIVERSITY
Faculty of Economics and Business
Administration
ACADEMIC YEAR 2013 – 2014
Macroeconomic Effects Of
Quantitative Easing
Evidence From The US
Master thesis to obtain the degree of Master of Science in Economics
Stef De Visscher
Supervised by
Prof. Gert Peersman
GHENT UNIVERSITY
Faculty of Economics and Business
Administration
ACADEMIC YEAR 2013 – 2014
Macroeconomic Effects Of
Quantitative Easing
Evidence From The US
Master thesis to obtain the degree of Master of Science in Economics
Stef De Visscher
Supervised by
Prof. Gert Peersman
Permission
I declare that the contents of this master thesis may be consulted and/or
be reproduced, provided the source is acknowledged.
Stef De Visscher
I
Samenvatting
In deze thesis wordt er na gegaan hoe onconventioneel monetair beleid werkt
en welke effecten dit heeft op de economie. Dit doe ik in twee stappen. Eerst
bespreek ik Nieuw Keynesiaanse modellen die toelaten onconventioneel
monetair beleid te analyseren in een economisch kader en ga ik in op de
transmissie kanalen. Daarna wordt er afgesloten met een eigen empirische
analyse.
Een eerste model van Gertler en Karadi (2011) introduceert een financiële
sector die de directe link tussen de huishoudens en de bedrijven breekt. De
hoeveelheid lonen die ze kunnen toekennen is echter gerelateerd aan hun
kapitaal. Bij een daling in de waarde van de lonen zal een groot stuk van het
kapitaal weg eroderen wat op zijn beurt uitmondt in een contractie van de
nieuwe leningen. Uiteindelijk zal dit leiden tot een daling van de investeringen
die nodig zijn voor de productie op peil te houden. Het zal dan ook in zo’n
geval dat een tussenkomst van de monetaire overheid gewenst is. Deze
laatste kan de economische dip verlichten door direct leningen te geven aan
de private sector.
In een tweede model, van Cúrdia en Woodford (2011), is de financiële frictie
van een andere soort. Hierbij is er een wig tussen de interestvoet die de
leners moeten betalen en de interestvoet die de spaarders ontvangen. Die
interest wig kan niet geëlimineerd worden. De reden hiervoor is dat financiële
instellingen kosten hebben. Een van die kosten zijn leningen die niet meer
worden terug betaald. Een stijging van die slechte leningen zorgt voor een
stijging van de kosten die uiteindelijk worden doorgerekend aan de leners en
een daling van de investeringen volgt. Opnieuw kan de monetaire overheid dit
verzachten door direct te lenen aan private agenten.
Uiteindelijk voer ik een VAR analyse uit waarbij ik na ga wat het effect is van
onconventioneel monetair beleid op de werkloosheid. Hierbij gebruik ik een
Cholesky decompositie om de gereduceerde residuen te ontleden. Hoewel er
problemen zijn met de identificatie strategie kan er worden besloten dat
onconventioneel beleid de werkloosheid kan drukken.
II
Acknowledgements
Heading towards the end of my master year, this dissertation will be the final
piece in order to obtain a master’s degree. Herein I will employ the acquired
knowledge and insights to justify my graduation.
Here I take the opportunity to thank the people that supported and guided me
through this thesis:
In first place I want to thank my promoter Prof. dr. Gert Peersman, he allowed
me to scrutinize a subject, which grasped my attention from day one onwards.
Special thanks go out to Marco Bernardini. Without his assistance, excellent
advice and hints I would have found myself in a considerable less comfortable
position.
Lastly, I like to thank Cédric Algoed and Steffie De Moor for reviewing my
thesis.
Stef De Visscher
III
Table of Contents
1! Introduction+.....................................................................................................+1!
2! New+Keynesian+DSGE+models+and+unconventional+monetary+policy+.................+3!
2.1! A!DSGE*model!augmented!with!a!financial!accelerator!........................................................!6!
2.1.1! The'model'...............................................................................................................................................'7!
2.1.2! Properties'of'the'model'.................................................................................................................'14!
2.2! Unconventional!monetary!policy!and!heterogeneous!households!................................!17!
2.2.1! The'model'............................................................................................................................................'17!
2.2.2! Properties'of'the'model'.................................................................................................................'23!
2.3! Irrelevance!proposition!.....................................................................................................................!24!
2.4! A!comparison!.........................................................................................................................................!26!
3! Unconventional+monetary+policy:+evidence+from+the+US+................................+28!
3.1! Related!literature!.................................................................................................................................!28!
3.1.1! The'impact'on'interest'rates'.......................................................................................................'29!
3.1.2! The'impact'on'macroeconomic'variables'.............................................................................'31!
3.2! Empirical!model!....................................................................................................................................!32!
3.2.1! Specification'of'the'VAR'model'..................................................................................................'32!
3.2.2! Identification'.....................................................................................................................................'35!
3.3! Estimations!and!results!.....................................................................................................................!36!
3.4! Robustness!Check!................................................................................................................................!39!
3.4.1! Is'the'model'stable'over'time?'....................................................................................................'39!
3.4.2! A'model'with'the'Industrial'Production'Index'....................................................................'40!
3.4.3! A'model'with'the'Stress'Index'.....................................................................................................'41!
4! Conclusion+......................................................................................................+42!
5! References+.....................................................................................................+43!
IV
List of Abbreviations
CDO:
Collateral Debt Obligations
CW:
Cúrdia and Woodford
GK:
Gertler and Karadi
MBS:
Mortgage Backed Securities
SLAP:
Large-Scale Assets Purchase
(S)VAR:
(Structural) Vector Autoregression
QE:
Quantitative Easing
V
List of Tables
TABLE 1: OVERVIEW LITERATURE STUDY ..................................................................................... 29
TABLE 2: OVERVIEW DATA .......................................................................................................... 34
VI
List of Figures
FIGURE 1: EVOLUTION HOLDINGS OF TREASURIES, MBSS, TERM AUCTION CREDIT......................... 2
FIGURE 2: IMPULSE RESPONSES AFTER A CAPITAL QUALITY SHOCK WITHOUT CREDIT POLICY .......... 15
FIGURE 3: IMPULSE RESPONSES AFTER A CAPITAL QUALITY SHOCK, WITH THE ZERO LOWER BOUND
AND CREDIT POLICY ........................................................................................................... 16
FIGURE 4: IMPULSE RESPONSES AFTER A SHOCK TO THE CREATION OF BAD LOANS, WITH THE ZERO
LOWER BOUND .................................................................................................................. 23
FIGURE 5: PLOTS OF THE NOMINAL AND TRANSFORMED DATA ....................................................... 33
FIGURE 6: IMPULSE RESPONSES MODEL I (ONE STANDARD DEVIATION) .......................................... 36
FIGURE 7: IMPULSE RESPONSES MODEL II (ONE STANDARD DEVIATION) ......................................... 37
FIGURE 8: ACCUMULATED IMPULSE RESPONSES OF INFLATION FOR RESPECTIVELY MODEL I AND
MODEL II ........................................................................................................................... 38
FIGURE 9: IMPULSE RESPONSES MODEL I (2003-2007) (ONE STANDARD DEVIATION) ..................... 40
FIGURE 10: IMPULSE RESPONSES MODEL I WITH INDUSTRIAL PRODUCTION INDEX (ONE STANDARD
DEVIATION) ....................................................................................................................... 41
FIGURE 11: IMPULSE RESPONSES MODEL I WITH STRESS INDEX (ONE STANDARD DEVIATION) ......... 42
!
VII
1
Introduction
As the financial crisis erupted in 2007, the economic outlook switched to
deeply depressive numbers. This challenged Central Banks around the world
as never before. Merely cutting policy interest rates was insufficient to
withstand the economic activity as the zero lower bound was hit.
Initially, the crisis was indicated by threats to the liquidity. As the anxiety in the
financial markets increased and the creditworthiness was readjusted, many
financial institutions were unwilling to lend to one another. In an attempt to
release some pressure from the financial markets, Central Banks around the
world drastically cut their policy rates. It was also then when first signs of nonstandard policies came at play. Ensuring the liquidity, the Federal Reserve set
up its Term Auction Facility. Contrary to normal times, depository institutions
could obtain necessary funds directly from the Federal Reserve instead from
primary dealers.
The damage, nonetheless, was done. The financial turmoil drove a wedge
between the interest rates - faced by the borrowers - and the policy rate. At
this stage the real economy was contaminated by the distressed situation,
which contributed to the period referred as the “Great Recession”. Combatting
the crisis, the Federal Reserve was constrained by the zero lower bound. In
order to facilitate the monetary stance in the economy, the Central Bank took
further steps, which can be broadly described as unconventional monetary
policy.
In response to the negative prospects and worsening labor market conditions
in 2008, the Federal Reserve announced its first round of large-scale asset
purchases (also referred to as QE1). By March 2009, it had purchased $1.75
trillion of assets, primarily MBSs. The economic recovery, however, was
sluggish. This induced the Federal Reserve to start with QE2 in November
2010. This time, a total amount of $600 billion of longer dated treasuries was
bought in order to compress long-term yields. On top of that the Federal
1
Reserve
announced
extension
program.
its
maturity
Herein
the
Figure 1: Evolution holdings of Treasuries, MBSs,
Term Auction Credit
Federal Reserve switched short-term
Treasuries
treasuries with long-term. Figure 1
4000000
shows the movement of the main
3500000
components that were used as policy
3000000
tool for quantitative easing.
2500000
MBSs
Term Auction Facility
2000000
Finally, in order to make financial
1500000
conditions more accommodative and
1000000
to facilitate lending to households,
500000
0
the Central Bank launched its third
round of asset purchases (QE3).
Every month a mixture of MBSs and treasuries were bought. In June 2013 the
Federal Reserve’s chairman Ben Bernanke announced the tapering of QE3.
Ultimately the program should be wrapped up mid-2014.
During the meltdown caused by the financial crisis, some academic problems
came to the surface. Stiglitz stated in 2011: “Those relying on the Standard
Model did not predict the crisis; and even after the bubble broke, the Fed
Chairman argued that its effects would be contained. They were not. In the
months that followed, policymakers floundered—and the Standard Model
provided little guidance as to what they should do.” Henceforth the latest
DSGE-models are required to deal with such deep downturns (Stiglitz, 2011).
In this thesis I will guide the readers through two models that embed the ability
to analyze unconventional monetary policies and that incorporate financial
institutions. The description can be found in section 2.
The rest of the thesis is structured as follows. In section 3 I estimate several
VAR models in order to analyze the Federal Reserve’s quantitative easing
during the last crisis. Finally, section 4 concludes.
2
2
New Keynesian DSGE models and
unconventional monetary policy
In this section a theoretical framework with the aim of analyzing
unconventional monetary policy is discussed. In order to do so I will briefly
explain two DSGE-models that embed the ability to analyze the exceptional
behavior of many Central Banks during the “Great Recession”. Those two
models proposed by Gertler and Karadi (2011) and Cúrdia and Woodford
(2011) will be the corner stone of this chapter.
Since many recent New Keynesian models are a simple extension of the basic
medium-size model, it is worth emphasizing the differences between the
standard model and the two models described later on.
DSGE-models provide a useful framework for economical analysis and are a
workhorse for monetary questions. One strong property of such a model is the
ability to describe the propagation mechanisms of exogenous shocks to the
economy. Moreover, they are very suitable to quantify the outcome of policy
actions (i.e. one could exploit it to forecast the outcome of policy changes)
(Tovar, 2009).
Here I use the Smets-Wouters (2003) model as the standard model. The
framework designed by the authors incorporates three entities: identical
households, identical firms and a Central Bank.
1. Households seek to maximize their lifetime utility. Hence they will
decide on how much to consume and save, how much to work and how
much to invest. A critical feature is that the households actually buy
capital and rent them directly to the firms. There are no frictions
involved in this process. As a consequence a financial sector does not
exist. In order to capture market imperfections, households have some
power in setting wages. One could think of labor unions, which
negotiate higher wages than they would have been if each worker
negotiated them separately. Moreover, wages are not perfectly flexible.
3
A possible explanation for this is the existence of contracts. To account
for this rigidity, workers can only reset their prices from time to time.
2. Firms produce consumer goods. As a matter of fact two sorts of firms
exist. First, intermediate firms attract capital and labor from the
households in order to produce intermediate goods. Since the
intermediate goods are no perfect substitutes, intermediate firms can to some extent - choose at which price to sell their products. In reality,
however, firms can only periodically reset their prices and not on a
continuous basis (e.g. menu costs). For the sake of this stylized fact,
the intermediate producer will only find itself once in a while in a position
where it could change its price. Second, the final goods producers
simply buy the intermediate goods and repackage them into final goods.
They operate in a perfect competitive market.
3. At the end of every period the intermediate goods producers are
obligated to pay a capital interest rate to the households. The capital
interest rate is the outcome of the interaction between the supply and
demand for capital.
4. Finally, the Central Bank uses a Taylor-rule to conduct its task of
stabilizing the economy. More specifically, the monetary government
reacts to output and price fluctuations. By altering the interest rate, the
monetary
government
can
influence
consumption,
saving
and
investment choices of private agents. Indeed, when interest rates are
low, households are tempted to consume and invest more since saving
is less attractive. Hence the Central Bank can change aggregate
demand and steer the economy.
Smets and Wouters (2003) took the model to the data and found that this
DSGE-model of that generation - with sticky prices and inflexible wages – was
rich enough to capture the behavior of the time series and to be used for policy
analysis.
4
As emphasized, the basic DSGE-model does not include financial frictions.
One convenient way to introduce financial frictions is the financial accelerator
mechanism (Bernanke, Gertler and Gilchrist, 1999). The main idea is that
some entities in the economy are constraint by the net worth of their balance
sheet. As a consequence the funds that an entity can obtain will be related to
its net worth. As it turns out, it will be hard for firms to obtain funds when their
balance sheets are impaired, even in times of low interest rates. The bottom
line is that firms may have other incentives and involve themselves in riskier
activities when their own net worth is low. The lenders, however, cannot
control for this. This agency problem will in fact deepen an economic crisis
since the net worth of the firms are typically procyclical. Indeed, in times of
downturns, firms’ profits will decrease and the prices of assets will decline.
Accordingly, firms will find it hard to attract external funding, which is
necessary for investment in capital. Such a situation could further impair the
balance sheets of firms. Consequently there is a chance of being trapped in a
vicious circle. The result is a more persistent downturn compared to a situation
with no frictions. There is empirical evidence that confirms the existence of a
financial accelerator mechanism (Christiano, Rostagno and Motto, 2010). The
model proposed by Gertler and Karadi (2011) will embed a financial
accelerator mechanism in a more realistic way. The details will be clarified in
the next subsection.
In the period up to the financial crisis, academic research usually focused
solely on the interest rate as the only monetary policy tool. Via open-market
operations the Central Bank could control the short-term interest rate. The
assumption was that all interest rates and asset prices were linked with each
other through arbitrage. Yet, some markets dried up during the “Great
Recession” and the linkage through arbitrage was broken (Blanchard,
Dell'Ariccia and Mauro, 2010). Moreover, Central Banks were constrained by
the zero lower bound. Many Central Banks responded to such an exceptional
situation by purchasing directly from the market. Such actions could not be
analyzed in a basic DSGE-model. The two models of Gertler and Karadi
5
(2011) and Cúrdia and Woodford (2011) have the appealing feature that they
insert the possibility to analyze this practice.
The remainder of this section is as follows. First Gertler and Karadi (2011) will
be explained. Second, I will briefly discuss the model by Cùrdia and Woodford
(2011). Third, I will come to the irrelevance hypothesis, which is an implication
of the model proposed by Cùrdia and Woodford (2011). Lastly, after the
discussion of both models, they will be shortly compared in a separate section.
2.1
A DSGE-model augmented with a financial accelerator
The model proposed by Gertler and Karadi (2011) has two main features:
1. It breaks the direct link between households and non-financial firms by
augmenting a standard model with financial intermediaries. Along with
this, the financial intermediaries are faced by a balance sheet
constraint, comparable to the financial accelerator mechanism. A sharp
decrease in the price of assets held by financial intermediaries will
impair their net worth and hence lead to a contraction of private lending.
The reasoning for this is that households are suspicious and do not trust
a financial intermediary with a high leverage. This gives them an
incentive to take away their deposits. Appealing to this approach is that
this model in se incorporates the balance sheet restrictions faced by
many financial institutions during the financial downturn.
2. Further, this model supports unconventional monetary policy by
allowing direct lending from the Central Bank to the private sector. In
times of turmoil, the balance sheet constraints faced by private
intermediaries tighten, increasing the gain from credit easing. Like this,
the authors want to capture the excessive purchase of MBSs. In the
following section I will briefly describe the model.
6
2.1.1 The model
This framework is an elegant extension of the New Keynesian standard model,
augmented with the presence of financial intermediaries. As noted above, the
funds that they can obtain will be determined by their net worth. As it turns out,
a negative shock to the quality of capital induces a significant larger downturn
compared to the standard model. In this illuminating way the authors introduce
a financial accelerator mechanism.
The economy exists of five types of agents and a Central Bank. The Central
Bank is authorized to conduct both conventional and unconventional monetary
policy. By unconventional monetary policy the authors mean direct lending to
the economy. The latter brings to mind the acquisition of MBSs by the Federal
Reserve.
2.1.1.1 Households
In the represented economy the households are identical, they work, consume
and save. They can save by buying one period government bonds and by
placing their savings with a financial intermediary for one period. Due to
arbitrage both options yield the same gross real return !! from time ! − 1 to !.
The household itself exists of two members: workers and bankers. Workers
simply supply labor and take their wages home to consume or save. The
bankers own the financial intermediaries and handover their earnings to their
household. When exiting from the market, a banker also takes home his
retained earnings. The decision problem will be standard. The household’s
utility function is as follows:
!
! ! ln !!!! − ℎ!!!!!! −
!!
!!!
!
!!!
!!!! !!(1)
1+!
Where 0 < ! < 1 is a discount factor and the parameter 0 < ℎ < 1 allows for
!
habit formation. The intertemporal rate of substitution for labor would be !.
7
The household, however, faces the following budget constraint:
!! = !! !! + Π! + !! + !! !! − !!!! !!(2)
Π! represents the profits transferred to the households from owning financial
intermediaries and non-financial firms, T! are lump sum taxes and B!!! is the
acquisition of short term debt (both deposits and government bonds). This is
nothing more than saying that in every period a household cannot consume
more than its resources.
If we assume that the marginal utility of consumption is given by ϱ! then the
first order conditions for labor supply and consumption are given by:
!
ϱ! !! = !!! !!(3)
!E! !!!! !!!! = !! !!(4)
First, equation (3) indicates that the household will find it optimal to supply
labor up to the point where the utility of the last hour worked will be exactly
offset by the disutility from it. Second, equation (4) denotes the optimal
consuming/saving behavior. Since the marginal utility is decreasing in the
amount of consumption, a rising interest leads to a lower level of consumption
at time t. Indeed, when the interest rate is higher, saving will be more attractive
and the household will postpone consumption.
2.1.1.2 Financial Intermediaries
Intermediaries collect funds from households and transfer them to nonfinancial firms. The introduction of this new entity breaks the direct link
between households and firms.
8
The balance sheet of an intermediary ! is given by:
!! !!" = !!" + !!"!! !!(5)
!!"!! denotes the deposits the intermediary ! obtains from the households. The
intermediary is obliged to pay the riskless return !!!! for the deposits. !!" is
the net worth of the intermediary and can be seen as the capital. Qt is the
relative price of a loan and !!" is the number of loans. Per period the
intermediary receives a stochastic return !!" for each loan. So every period
the net worth grows by:
!!"!! = !!"!! !! !!" − !!!! !!"!! !!(6)
And by substituting (5) into (6):
!!"!! = !!"!! − !!!! !! !!" + !!!! !!" !!(7)
The growth of the net worth depends on the riskless return !! , but more
importantly on the total quantity of assets held by the intermediary !! !!" and
the premium !!"!! − !!!! .
It is obvious that by expanding the balance sheet indefinitely the intermediary
will maximize its net worth. To prevent this, Gertler and Karadi (2011) included
an agency problem. Each period the intermediary has the possibility to redirect
a fraction, ! , of its obtained deposits to its household. The depositors,
however, can force the bank into bankruptcy if they decide that the diverted
fraction is too large.
For depositors willing to supply funds to the intermediaries, the following
incentive constraint must be fulfilled:
!!" ≥ !!! !!" !!(8)
9
The left hand side represents the cost of bankruptcy whereas the right hand
side represents the gain of diverting a fraction of its funding. !!" can be
rewritten as:
!!" = !! !! !!" + !! !!" !!(9)
Here is !! the marginal utility of holding assets (increasing in the interest
premium) and !! is the marginal utility of holding capital. As it turns out the cost
of bankruptcy equals the utility the intermediary gets from holding assets and
capital. It will be rational for the intermediary that the incentive constraint binds
with equality. Accordingly the link between assets held and capital is given by
(by substituting (9) into (8)):
!! !!" =
!!
! = !! !!" !!(10)
! − !! !"
The leverage ratio is then given by !! . Since all intermediaries are identical the
total demand for is assets is:
!! !! = !! !! !!(11)
According to (11) the total amount of capital that the financial sector can lend
to the firms for investment purposes is positively related to the capital. Doing
so, the reasoning underneath the financial accelerator mechanism is
introduced. Imagine a shock to the quality of assets hitting the economy and
asset prices would decrease. Capital of the banks would fall and provoke a
credit crunch.
10
2.1.1.3 Intermediate goods firms
Every period a firm needs to buy capital goods, !!!! , to produce goods in the
next period. In the subsequent period the firm sells the left over capital on the
market. In order to buy those capital goods a firm needs to obtain funding from
the financial intermediaries. Thus, the following entity must hold all the time:
!! !!!! = !! !! !!(12)
Equation (12) is of key importance. This gives the direct link between the firms
and the financial intermediaries. If for some reason the price of capital would
decrease, then it will directly impair the worth of the total loans held by the
financials.
Two assumptions are made. First, there are no frictions for intermediate goods
firms during the process of obtaining funds. Second, the financial intermediary
is fully informed and therefore no problems are involved with payoffs. The
intermediate goods producers are not explicitly constrained in obtaining funds
but they are, however, implicitly constrained by the asset demand of the
financial intermediaries. To this extent the firms are as well affected by the
financial accelerator mechanism.
At time ! the firms produce output following a Cobb-Douglas function variant:
!! = !! (!! !! !! )! !!!!
!!(13)
!
Here !! stands for the quality of capital and along with this !! !! is the effective
quantity of capital. !! , !! , and !! respectively are the state of technology,
utilization rate of capital and labor employed.
11
As the intermediaries work in a perfect competitive market they make no
profits. Therefore the return on capital equals the interest rate the firms have to
pay to the financial intermediaries. The ex post interest then is given by:
!!"!! =
!!!! + (1 − !)!!!!
!!!! !!(14)
!!
The return is higher when the gross profit per unit capital, !!!! , is higher.
Further, the return is higher when the quality of capital, !!!! ,is higher and when
the rest value, (1 − !)!!!! , is higher. Here is ! the depreciation rate. Important
note, by solving equation (14) to !! it is clear that the current asset price
depends on the beliefs on the quality of capital in ! + 1. Thus, an expected
decrease in the quality of assets would already have an impact on the
economy’s output today.
2.1.1.4 Capital producing firms
When the intermediate goods firms use capital, the competitive capital firms
buy the left over capital stock and repair it. Besides that they also produce new
capital. We can therefore denote the production of new capital as if it were net
investment ( !!" + !!! !! = !! ). The refurbishing of capital is costless. The
production of new capital, however, is not. This implies that the price of new
capital increases as investment increases.
The implementation of capital adjustment cost is done in order to make
investment less sensitive for the interest rate and to improve the fitting to the
data (Christiano, Eichenbaum and Evans, 2001).
2.1.1.5 Retail Firms
The only function of retail firms in the economy is simply to repackage the
goods, made by the intermediate goods producers, and to sell them to the
households. The main characteristic is that the retailers can only periodically
change their prices. The firms that cannot re-optimize their price will index it to
12
the lagged inflation rate. The firms that are able to change their price will set it
in order to maximize the discounted sum of current and future profits.
2.1.1.6 Central Bank
Conventional Monetary Policy
The monetary government conducts the conventional monetary policy using a
Taylor-rule:
!! = 1 − ! ! + !! !! + !! (!"#!! − !"#!!∗ ) + !!!!! + !! !!(16)
Here, !! is the nominal interest rate, !! is inflation, !!∗ is the natural level of
output, ! the steady state nominal interest rate and ! is a smoothening
parameter between zero and unity.
Moreover, the following relation gives the link between the nominal interest
rate and the real interest rate:
1 + !! = !!!!
!! !!!!
!!(17)
!!
Unconventional Monetary Policy
If the financial sector is impaired the Central Bank can opt to issue loans to
non-financial firms. The Central Bank can finance this by issuing government
debt on which it pays the riskless return !!!! . On the amount lent to the nonfinancial firms, the monetary government receives the stochastic interest !!"!! .
In contrast with the private financial intermediaries there is no chance of a
Central Bank default. This implies that the Central Bank’s balance sheet is not
constrained by a leverage ratio. The Central Bank, nonetheless, faces an
efficiency cost of τ per loan. In this fashion the model recognizes the expertise
of financial intermediaries. As a consequence it is optimal that only the private
sector intermediates in normal times.
13
Ultimately the total worth of loans in the economy is given by
!! !! = !! !! + !! !! !! = !!" !! !!(15)
Where !! is the fraction of the loans issued by the Central Bank. The Central
Bank can independently choose !! . As a result the Central Bank can alter the
general leverage ratio positively by giving loans to non-financial firms.
The monetary government chooses !! !by the following feedback rule:
!! = ! + !!! !"#!!"!! − !"#!!!! − (!"#!! − !"#$) !!(18)
When the government expects a rise in the interest spread, the fraction of
intermediation will increase. Here (!"#!! − !"#$) is the steady state interest
spread, and ! is a policy coefficient.
2.1.2 Properties of the model
Gertler and Karadi (2011) show the effect of a negative shock to the quality of
capital without credit policy (Figure 2). By doing this they want to capture the
broad dynamics of the recent crisis. This in fact relates to the deterioration of
many MBSs, CDOs and other assets in the middle of the crisis. The impulse
responses are given for both the standard New Keynesian model and for the
model described by Gertler and Karadi (2011). As we expected, the downturn
becomes more severe due to the existence of the financial accelerator.
The reasoning is as follows:
1. The deteriorating capital causes a plunge in output. Subsequently, the
demand for capital of the firms will decline, lowering asset prices and
increasing interest rates.
2. There is, however, a second round effect. Owing to the downward
evolution of asset prices, the balance sheets of the bankers will be
affected negatively. Since the bankers are constrained by a maximum
leverage, the demand for new loans will drop and a credit crunch is the
result. Even when the shock is vanished, the firms cannot fully obtain
14
new funds. The rationale for this is that, due to the financials’ impaired
balances, it takes time to restore them. In the meantime the financial
intermediaries have to decrease their lending. Indeed, the second round
effect is a consequence of the financial friction introduced in this new
model.
Figure 2: impulse responses after a capital quality shock without credit policy
Source: Gertler & Karadi (2011), p28
The model is calibrated so that in steady state the nominal interest rate is 4
percent. In Figure 2, however, the nominal interest rate drops with 500 basis
points. This implies a negative nominal interest rate. Figure 3 gives the results
when the zero lower bound is binding. There are also two more graphs
included, one with aggressive credit policy and one with moderate credit
policy. In Figure 3 it is obvious to see that credit policy is able to significantly
15
soften the economic downturn. The monetary government succeeds to
mitigate the sharp rise in credit spreads. The Central Bank acts as a substitute
for the weakened financial intermediaries. This fosters investment and reduces
the slump.
Figure 3: impulse responses after a capital quality shock, with the zero lower bound and credit
policy
Source: Gertler and Karadi (2011), p.31
16
2.2
Unconventional monetary policy and heterogeneous
households
Cúrdia and Woodford (2011) recently developed another prominent New
Keynesian model. Even though the presented model is a rather highly
simplified representation of the reality, it embraces some noteworthy features
that will be portrayed later on:
1. The model deviates from the general belief of one representative
household. Instead the authors introduce two types of households:
savers and borrowers. Here they cannot contract with each other but via
a financial intermediary. Though, there will be some financial frictions
involved in this process.
2. The policy rate of the Central Bank is defined as the interest rates paid
on deposits. The Central Bank, however, can only influence this
indirectly. The sole way to steer the policy rate is by altering the interest
rate the financial firms receive on their reserves, held with the Central
Bank, and by affecting the amount of reserves they hold. In this
attractive way Cúrdia and Woodford (2011) capture the transmission
mechanism faced by Central Banks in reality.
3. Further, the Central Bank can use its balance sheet in two ways. It can
simply expand its balance by purchasing treasuries. Alternatively, the
Central Bank can involve itself in private lending in times of financial
distress. It may be clear that this is the unconventional behavior of the
Central Bank.
2.2.1 The model
The economy consists of households, firms, financial intermediaries and a
Central Bank. For the sake of simplicity the monopolistic firms only use labor to
produce goods and along with this simplification the production merely
consists of consumption. As a consequence capital and investment do not
come into to play. The households, however, are heterogeneous. More
specific, the households are divided between borrowers and savers. The
17
borrowers and savers cannot interact with each other but via a financial
intermediary. Yet, there are some frictions involved when savings are
transferred to the borrowers.
2.2.1.1 Households and Firms
In contrast with the standard model, Cúrdia and Woodford (2011) does not
make use of a representative household. As an alternative there are two types
of households: borrowers and savers.
One could argue that, over time, borrowers will build up masses of debt and
savers will build up masses of unused consumption. To prevent this, every
period a household’s type may change with probability 1 − ! . When that
occasion arrives the new type will be ‘borrower’ with probability !! and ‘saver’
with probability !! .
Each period both types of households maximize their utility knowing that the
total utility is increasing in consumption and decreasing in labor supply. In the
optimum the impatience of consumption for borrowers exceeds the impatience
of consumption for savers for the same level of consumption. This translates
into a higher marginal utility of expenditures for borrowers.
In a model without financial intermediaries, money would flow from savers to
borrowers given the interest rate. This process would continue until the
marginal utility of expenditure equals for both types. The savers would be more
than pleased to postpone their consumption and receive a compensation from
the borrowers. On the other hand, the gain of consuming now, for the
borrowers, will be higher than the loss from paying interests. Hence both would
win from such a situation.
In this model, however, savers and borrowers cannot contract with each other
but through the financial intermediaries. As a consequence borrowers face
another interest rate (!! ) than the savers (!! ) due to financial intermediation.
18
The Euler equation for each type is given by:
!!! = !!!
1 + !!!
! + (1 − !)!! !!!!! + (1 − !)!! !!!!! !!(19)
Π!!!
!!! = !!!
1 + !!!
!
! + (1 − !)!! !!!!
+ (1 − !)!! !!!!! !!(20)
Π!!!
Given the costs the financial intermediaries face, !!! will always be higher than
!!! .
Finally, all firms are monopolistically competitive suppliers. The production
function is a simple function with only labor and technology. The model
assumes a Calvo-style staggered price adjustment.
2.2.1.2 Financial intermediaries
Financial intermediaries’ liabilities consist of deposits. The assets on the other
hand are composed of loans and reserves. On the deposits the intermediary
pays a nominal return!!! , on the loans they demand an interest rate !! . For two
reasons the spread between !! and !! will not be eliminated:
1. A part of the loans are bad. The fraction of loans that is impaired is
given by !! (!! ). Those loans will not be repaid and thus are a cost.
2. Issuing loans consumes real resources !!! (!! ; !! ). These resources are
!
increasing in !! and decreasing in the quantity of reserves !! (!!"
≥
!
0, !!"
≤ 0). The authors of this model further suppose that there exists a
level of reserves !! ! where the cost can no longer be reduced by
expanding the reserves.
They further receive a return (!! ) on their reserves held with the Central Bank.
Since financial intermediaries are competitive, the following equation must hold
with equality all the time:
1 + !!! !! + 1 + !!! !! = 1 + !!! !! !!(21)
19
It is clear that the intermediary faces a trade-off. On the one hand, holding
reserves reduces the cost of lending; on the other hand there is an opportunity
cost as !!! ≤ !!! .
The deposits that are not used for originating loans or reserves are distributed
to the shareholders.
!! − !! − !! − !! !! − !!! !! ; !! !(22)
In the end the financial intermediaries want to maximize their earnings. Doing
so leads to the following two first-order conditions.
!
!!"
!! ; !! + !!" !!
!
−!!"
!! ; !! =
!!! − !!!
= !! =
!(23)
1 + !!!
!!!
!!! − !!!
=
!(24)
1 + !!!
Equation (23) tells us that the interest spread must be high enough to cover
the marginal cost of issuing loans. According to equation (24) the financial
intermediary will hold reserves up to the point where the cost of holding
reserves equals the marginal profit of doing so.
2.2.1.3 Central Bank
The liabilities of the Central Bank consist of reserves on which it pays !!! . With
those reserves (!! ) the Central Bank acquires government debt and issues
!"
loans to households ( !!"
! ). Hence the balance sheet is given by: !! +
Treasuries = !! . One could conclude that !! is the monetary base in this
model. The Central Bank can influence the reserves and independently
choose the level of lending to the private borrowers. Further, the interest paid
!
on !!"
! equals to !! . Issuing loans to borrowers consumes real resources
!!!" (!!"
! ).
20
The Central Bank can influence !!! (its policy rate) in two ways. First, by
purchasing or selling treasuries, the Central Bank can alter !! .1 Lowering !!
will raise the marginal profit of holding reserves by the intermediaries. The
financial firms know that holding more reserves will actually lower their costs.
The banker will increase !!! to attract more funding to compensate for the
restrictive action by Central Bank, hence !!! will widen.
Second, by varying !!! it can change !!! for a given!!!! . If !!! is lowered then !!!
will follow to keep !!! at the same level. Since reserves are financed by
deposits and !!! > !!! , holding reserves implies an opportunity cost. If the
Central Bank chooses to lower !!! , that cost will increase and exceed the
benefits from holding reserves. Therefore the financial intermediary must lower
!!! to restore that equilibrium.
The Central Bank can conduct monetary policy in three ways (ignoring the
interest-rate policy). First, there is the reserve-supply policy, this implies a
target for the interest rate paid on the financial intermediaries’ reserves.
Second, by expanding the balance sheet of the Central Bank. Third, there is
the credit policy by which is meant that the Central Bank can independently
choose its lending to the private sector.
Reserve-supply policy
The goal of the Central Bank is to maximize the welfare. The Central Bank can
do this by lowering the real resources consumed by the financial
intermediaries. Earlier it was clear that the real resources consumed by
financial intermediaries was decreasing in the amount of reserves held. If !!! is
positive, there exists a cost. The existence of costs will lower the incentive of
banks to hold reserves. As it turns out an optimal reserve-supply policy
requires that !!! equals to zero all times. Indeed, the Central Bank should set
1
Since treasuries and deposits yield the same interest rate, savers will not alter their behavior.
When e.g. the Central Bank buys treasuries from the savers, the savers will increase their
deposits. For a given amount of loans, the reserves of the financials will increase.
21
the interest rate paid on reserves, !!! , equal to its policy rate !!! . The bank of
New Zealand already uses this implication. More specifically, the interest paid
on overnight balances is the policy rate itself.
Quantitative easing
Here we assess what the influence is of pure quantitative easing in this model.
By pure quantitative easing is meant an increase in reserves, which in turn
finances the purchase of treasuries, by the Central Bank.
One can be clear about this. While it is harmful to lower the reserves below
!! ! , it is ineffective to increase reserves beyond !! ! . If !!! equals to zero,
the real resources consumed by the financial intermediaries can no longer be
decreased by further expanding the reserves.
There are, however, two exceptions. It can be necessary for the Central Bank
to increase reserves when it is willing to expand its lending to the private
sector. This is a simple implication of the balance sheet. Second, an expansion
of the balance sheet could be a signal that future short interest rate will be
lower than normal. This will induce rational agents to alter their expectations.
Credit policy
Now we take as given the size of the Central Bank’s balance sheet. When
credit policy is conducted, the Central Bank will lower its holdings of treasuries
and increase its lending to the private sector. Once the Central Bank increases
its lending, the issuing of loans by the private intermediaries will decrease. As
a fact the real resources will also decrease. Moreover, the interest rate margin
(!! ) will too decrease as the costs of the financial intermediaries fall.
One can assume that it is optimal for the economy if the Central Bank issued
all the loans in the economy. It is not realistic to think that the Central Bank
would have a competitive advantage over financial intermediaries. As noted
earlier the Central Bank also consumes real resources. It is further assumed
that there is an initial cost for the Central Bank when it issues loan. So in
22
normal times !!"
! = 0. Only when the financial intermediaries are severely
impaired it is desirable that !!"
! > 0.
Conventional monetary policy
It is further assumed that the interest-rate policy is conducted following a
Taylor-rule of the form:
!!! = ! ! + !! !! + !! !!
Here ! ! is steady-state real policy rate, !! is inflation and !! is a measurement
for the deviation of ! from its naturel level.
2.2.2 Properties of the model
Figure 4: impulse responses after a shock to the creation of bad loans, with the zero lower bound
Source: Cúrdia and Woodford (2011), p. 76
Herein we look how the model behaves when there is an exogenous increase
in the bad loans. Such a shock is relevant as it is comparable to the bust of the
23
subprime bubble. Figure 4 gives the impulse responses. The dimension of the
shock is such that the zero lower bound is reached. One can see that in
absent of credit policy, output would shrink more than ten percent. Due to the
impaired loans, the costs the financials face incraese, those costs are then
tranfered which leads to a sharp increase in the credit spread and borrowers
will borrow less. The modest rise in consumption of the savers, stemming from
the fact that the Central Bank lowered its policy rate, is not enough to eliminate
the massive decrease of consumption by the borrowers.
If there is an optimal credit policy the Central Bank could be a substitute for the
severely impaired financial intermediaries. It prevents the credit spread from
increasing sharply compared to the case with no credit policy. By involving in
private lending the Central Bank can reduce the cost the financial
intermediaries face. As a result the borrowers’ consumption contracts their
consumption only a little bit.
2.3
Irrelevance proposition
As stated by Cúrdia and Woodford (2011), massively purchasing of one period
treasuries by the Central Bank will have no real effect on the economy’s
output. As treasuries and deposits are perfect substitutes people are indifferent
between both. Hence they will not change their optimizing behavior.
Eggertsson and Woodford (2003) refer to the existence of an irrelevance
proposition. The sole real effect stems from the fact that by buying masses
amounts of government bonds, the rational agents will modify their beliefs on
future monetary policy. This is often referred to as the signaling channel.
In practice the Federal Reserve bought stacks of government bonds. Bowdler
and Radia (2012) argue that the Federal Reserve and the Bank of England
focused their acquisitions not exclusively on short-term bonds. As bonds with
longer maturity are typically to found an imperfect substitute for money, a
portfolio rebalancing channel comes into play. This will be explained next.
24
Following Bauer and Rudebusch (2011) it is possible to decompose the
interest rate on a fixed income asset of ! years:
!! = !!,! + !
!! = !!,! + !!"#$%$&# + !!"!#
The yield on a fixed income asset equals the risk free yield plus a term
premium, !. Then we can rewrite the term premium into a specific interest rate
risk premium and an idiosyncratic risk premium. The interest rate risk premium
is a result of the risk aversion behavior of the investors. Since the price of a
fixed income asset is affected by future short-term interest rate evolutions,
investors will demand a premium to bear the risk (Bowdler and Radia, 2012).
The idiosyncratic premium, on the other hand, reflects, for example, supply
and demand imbalances for that particular asset.
Many institutions (like pension funds) try to match the maturity structure of their
liabilities with the maturity structure of their assets. More specific, pension
funds prefer to hold almost risk free long-term government bonds. By giving
those institutions money instead, they are moved away from their preferred
habitat (Bowdler and Radia, 2012). As a consequence of the intervention of
the Central Bank, the aggregate supply of long-term government bonds is
restricted. The demand, however, is not. Henceforth the investors are willing to
accept a lower idiosyncratic risk premium to stay in their preferred habitat. This
channel can be termed as the local supply channel. The bottom line is that the
long-term interest rate will decline.
The previous paragraph emphasizes the adjustment on the individual level.
There will, however, be a connection with other fixed income securities. If a
Central Bank buys government bonds with longer maturity it decreases the
aggregate amount of duration risk, reflected by the interest rate risk premium.
Hence the private sector will request a lower interest rate due to the falling
premium. Yet there are some objections to this duration channel. Woodford
(2012) underlines that the purchasing of long-term government bonds will not
25
lead to a lower risk level in the economy as a whole. The risk is simply
transferred to the Central Bank. If one were to expect lower Central Bank
revenues due to the increase in risk, one would consume less to compensate
future taxes. This would cancel out the positive effect of lower long-term
interest rates. Then again the assumptions for such a Ricardian reaction are
rather strong (Bowdler and Radia, 2012).
Estimations of D’Amico et al. (2012) indicate that both the local supply and
duration channel were of major importance during the latest LSAPs. More
specifically, they find that both channels lowered treasury yields by 35 basis
points for QE1 and 45 basis points for QE2. Along with their findings they
suggest that new theoretical models need to capture preferred habitat
elements in order to capture the transmission of unconventional policy. Some
work has already been done. E.g. Cúrdia and Ferrero (2013) extend a basic
DSGE-model with preferred habitat elements.
2.4
A comparison
Up to now I have discussed two models that embed the ability to analyze
unconventional monetary policy. It is not my intention to highlight all the
differences between the two models. In the light of my thesis I will only cite
those that are relevant.
The models have the property that they both include financial intermediaries.
The financial frictions in the two models, however, are very different. Whereas
the financial intermediaries in the CW-model face some costs in originating
loans, the friction in the GK-model consists of a financial accelerator
mechanism. The latter embeds a realistic characteristic: the financial
intermediaries are constraint by their capital. To put it differently, the inverse of
the leverage ratio in the GK-model brings to mind the minimal capital
requirements in reality.
When the Central Bank decides to conduct unconventional monetary policy, in
the CW-model, it can use two balance sheet operations: purchasing treasuries
26
or lend to the private sector. One major conclusion was that simply buying
treasuries would have no effect once the reserves exceed a certain amount.
Henceforth there is only one effective unconventional instrument for the
Central Bank: direct lending to the private sector. To this extent the CW-model
is very similar to the GK-model. Although the Central Bank in the GK-model
has not the possibility to hold treasuries, it can lend directly to private firms.
The construction of the financial shocks in both models is unalike. In the GKmodel a financial shock is defined as a deterioration of the quality of capital
while in the CW-model it is defined as an increase in originating bad loans.
Yet, both shocks lead to something equivalent: a contraction of the private
lending. In the GK-model this pops up as a lower level of loans granted. The
cause of the credit crunch in the CW-model is a sharp increase in the interest
rate the borrowers face.
As noted above, the Central Banks in both models can directly lend to the
private sector in time of financial turmoil. A drop in the quality and prices of
capital causes the large downturn in the GK-model. Even though the Central
Bank acts as a substitute for the financial intermediaries, this will not prevent
the waning investments. Such a channel is not possible in the CW-model, as it
does not include a capital stock.
Finally, a tempting feature of the CW-model is that the monetary government
cannot directly influence the policy rate. The Central Bank can only succeed to
steer the deposit interest rates by altering the monetary base or by altering the
interest paid on that monetary base. In some extent this resembles the
repurchasing agreements, which are common in practice. In the GK-model
such a transmission does not take place. There it is simply assumed that
Central Bank can directly influence the interest rates on deposits.
27
3
Unconventional monetary policy: evidence from
the US
In this section I want to investigate whether the balance sheet operations of
the Federal Reserve were able to support employment. I do this by employing
a Structural Vector Autoregression (SVAR) where the model is identified with a
Cholesky decomposition.
First, I give an overview of the existing literature. Herein I make a distinction
between studies that mainly focus on interest rates and those that focus on
macroeconomic variables. Second, I discuss my model, the identification
strategy and the main results.
3.1
Related literature
The existing empirical literature suggests that the unconventional practices of
the Federal Reserve during the “Great Recession” supported real activity.
The direct objective of unconventional monetary policy is to lower long-term
interest rates (Krishnamurthy and Vissing-Jorgensen, 2011). The ultimate goal,
however, is to foster economic activity and to encourage employment.
Although a substantial part of the empirical literature only focuses on the
reaction of 10-year treasury yield to unconventional balance sheet expansions,
there are, nonetheless, some caveats from such a method.
While it is likely that lower interest rates would have led to higher real GDPgrowth, the sensitivity of the economy to interest rates may have changed
during the “Great Recession”. When consumers and firms are confronted with
job losses, foreclosures, reorganizations and bankruptcies it is highly
implausible that the interest rate sensitivity would be the same compared to
normal times. As a consequence the lower interest rates, induced by
quantitative easing, would have had a more modest impact (Putnam, 2013).
Conclusions on the macroeconomic effects of quantitative easing based on
studies that merely focus on long-term interest rates, could give a distorted
28
view. Therefore it is worthwhile analyzing the effects of quantitative easing
directly on macroeconomic variables. A brief overview of the empirical
literature can be found in Table 1.
Table 1: overview literature study
Study
Method
Sample/Period
Results
D’Amico and
King (2010)
Event-study
First $300 billion
Lowered 10-year yield with
50 bp
Gagnon et al.
(2011)
Event-study
First $1725 billion
Lowered 10-year yield with
91 bp
Christensen and
Rudebusch
(2012)
Event-study
First $1725 billion
Lowered 10-year yield with
89 bp
Gagnon et al.
(2011)
Time Series
December 2008 March 2010
Lowered 10-year yield with
38 to 82 bp
OLS
January 2009 –
June 2009
Lowered 10-year yield with
39 bp
November 2008 –
September 2011
Compressed 10-year yield
but is reversed in
subsequent months
Doh (2010)
Wright (2013)
SVAR
Time Varying
VAR
1965-2009
1% spread shock leads to a
1.9% increase in GDP
growth but vanishes
Gambacorta et
al. (2013)
SVAR
January 2008 –
June 2011
3% increase of the balance
sheet leads to a 0.05-0.15%
increase of GDP but
vanishes
Cúrdia and
Ferrero (2013)
DSGE Model
$600 billion
purchase of
treasuries
Boosts GDP growth with
0.13%-point and fades
away
Large-scale
Model
QE1 and QE2
Increases GDP with 3% in
the second half of 2012
Baumeister and
Benati (2010)
Chung et al.
(2011)
3.1.1 The impact on interest rates
Different methods have been used to study the effects of quantitative easing
on interest rates. Yet, they all lead to the same conclusion: quantitative easing
succeeded to lower 10-year government bond yields.
29
One group of studies made use of event-studies. An event-study is a statistical
method to assess the behavior of a variable on certain key dates. More
specifically, one looks at the 10-year government bond yields on dates that
were accompanied by announcements concerning unconventional monetary
policy. Although event-studies are straightforward, they have some drawbacks.
First, the results could differ by changing the window or key dates. Second, the
announcements took place during turbulent times. There may be a chance that
interest rates were further affected by other news (Wright, 2013).
Gagnon et al. (2011) finds that the first acquisition of $1.725 trillion of assets
lowered the 10-year treasury yield by 91 bp. Moreover, they show that those
effects were transferred to other sorts of assets, including agency debt. These
results are very similar with those obtained by Christensen and Rudebusch
(2012). The latter study, using the same key dates, shows that the 10-year
treasury yield declined by 89 bp. The authors, however, highlight that it is
possible that an event-study is likely to underestimate the effects on later key
dates. An explanation is that the market could have anticipated the new
events. A study by D’Amico and King (2010) investigated the purchase of the
first $300 billion of treasuries. This study finds that this operation compressed
the 10-year treasury yield with 50 bp. This suggests that the effects of
subsequent actions were underestimated or less effective.
Using the ‘Ordinary Least Squares’ estimator could sidestep some of these
problems. Studies employing this methodology find somewhat reduced results.
Gagnon et al. (2011) took the same period as their event-study and found a
downward pressure on the 10-year treasury yield ranging from 38 to 82 bp
while Doh (2010) found a decline of 39 bp.
Finally, a VAR approach implies that the theoretical structure on the data is
very limited (Peersman, 2011). Wright (2013) attempts to assess the effects by
using such a VAR. His main result is that quantitative easing is successful in
lowering 10-year treasury yields but the downward pressure is quickly
reversed in the subsequent months.
30
3.1.2 The impact on macroeconomic variables
Taking into account the lags it takes for output to react to policy changes, an
event-study is not an appropriate tool to study the effects of quantitative easing
on inflation or output. For this reason the use of VAR-, DSGE- and large-scale
models might represent a better strategy.
One of the first papers scrutinizing the macroeconomic effects of the Fed
Reserve’s LSAPs was one of Baumeister and Benati (2010). By using a time
varying VAR model they define unconventional monetary policy as a ‘spread
shock’. A ‘spread shock’ is determined as a compression of the 10-year
treasury yield, caused by quantitative easing, keeping the policy interest rate
constant. The study finds that after a 1% negative shock to the 10-year
treasury spread, the real GDP growth is 1.9% higher after 3 quarters and
vanishes subsequently after 2 and a half years. Likewise real GDP growth,
inflation reaches a peak after 3 quarters of 1,1%. Inflation, however, is more
persistent and dies out after 3 and a half years. Based on the estimations they
find that GDP growth would have been -10% in the first quarter of 2009 with
inflation reaching just below zero.
Again, by carrying out a VAR approach Gambacorta, Hofmann and Peersman
(2013) find evidence that, after a 3% exogenous increase of the Federal
Reserve’s balance sheet, the level of real GDP mounts with 0.05-0.15% after 6
months to return to zero after 18 months. The price level is boosted with 0.040.10% after about 8 months and depicts a sluggish return.
To conclude this section I refer to studies that exploit theoretical models in
order to simulate the effects of a balance sheet expansion. Cúrdia and Ferrero
(2013) make use of a DSGE-model that embeds the preferred habit formation
hypothesis. The authors point out that a $600 billion purchase of treasuries
would boost GDP growth with 0.13%-point and fades away after 2 years. The
results, nonetheless, are sensitive for the degree of investor segmentation.
Chung et al. (2011) also investigated QE1 and QE2. After simulating those two
programs with the FRB/US macroeconomic model, augmented with a simple
31
model of portfolio balance effects, they conclude that the level of real GDP was
raised by 3% in the second half of 2012 due to quantitative easing.
3.2
Empirical model
3.2.1 Specification of the VAR model
In order to analyze the effects of exogenous balance sheet shocks on the
economy, a standard monetary VAR model is augmented with two new
variables. Hence, the following reduced form VAR model is estimated:
!! = ! + !!" + ! ! !!!! + !!
Where !! is a vector of endogenous variables, composed of the unemployment
rate (!! ), the monthly inflation rate (!"#! ), the VIX index (!"#! ), the Federal
Funds rate (!!! ) and the Balance Sheet (!! ). ! is a vector of intercepts, !" is a
deterministic trend, ! ! is a matrix polynomial of autoregressive coefficients
and !! is a matrix of the reduced-form error terms.
Here the structural model is given by the following equation:
!! !! = ! + !!" + ! ! !!!! + !!!
Herein !! is the identity matrix and ! represents the cholesky factor. Now the
reduced-form error terms are composites of the structural error terms !! , they
are related to each other via the following equation:
!! !! = !!!
All data is drawn from the Federal Reserve Economic Database (FRED) and is
expressed on a monthly basis. The length span is from January 2007 till
December 2013. A plot of the data and a summary of the transformations can
be found in Figure 5 and Table 2.
The state of the economy is reflected by the unemployment rate and the
inflation rate. The former two variables will capture the macroeconomic effects
of quantitative easing.
32
As in Gambacorta et al. (2013) a proxy for market instability, the VIX index, is
entered into the model. The inclusion of such a variable cannot be
underestimated. The economic meltdown during the second half of 2008 was
initially induced by an unstable financial system. Moreover, in late November
(2008), the Federal Reserve announced its acquisition of MBSs as an
endogenous reaction to the financial turmoil (Gambacorta et al., 2013).
Omitting a proxy for financial instability could falsely lead to the conclusion that
the expansion of the Central Bank’s balance sheet caused a contraction in
economic activity.
The conventional instrument of monetary policy is represented by the Federal
Funds interest rate. Contrary to Gambacorta et al. (2013) I do include this
variable because my model is estimated over a substantial longer length span.
In this longer period the interest rate was actively used in order to steer the
economy.
Lastly, the total balance sheet is included into the model. The balance sheet
catches the unconventional behavior of the Federal Reserve as it exploded
during the last crisis. This variable is supposed to reflect al the non-standard
actions by the Federal Reserves, including direct lending to financial
institutions and purchases of public and private paper. After the variable is
expressed in real per capita terms I take the natural logarithmic. As the
balance sheet depicts an upward tendency, a trend is included into the VAR
model.
Figure 5: plots of the nominal and transformed data
Unemployment
12,0
Inflation
1,5
10,0
1
8,0
0,5
6,0
4,0
0
-0,5
2,0
-1
0,0
-1,5
-2
33
VIX
FF
70,00
6,00
60,00
5,00
50,00
4,00
40,00
3,00
30,00
2,00
20,00
10,00
1,00
0,00
0,00
Real Balance Sheet Per Capita
14000
12000
10000
8000
6000
4000
2000
0
Table 2: overview data
Variable
Balance Sheet
FRED CODE
WALCL
Transformation
!"(
!"#"$%&!!ℎ!!"!
)
!"#$%&'(")! !!!"#!
FEDFUNDS
!
INDPRO
!"(!"#$%&'()*!!"#$%&'(#)!!"#$%)!
CPIAUCSL (CPI)
!" !"#!!! − !"(!"#!) !
MBST
!
STLFSI
!
WTERAUC
!
Treasuries
TREAST
!
Unemployment
UNRATE
!
VIX
VIXCLS
Monthly Averages!
Federal Funds Rate
Industrial Production Index
Inflation
MBSs
Stress Index
Term Auction Credit
34
3.2.2 Identification
Ultimately I try to grasp the effects of exogenous innovations to the balance
sheet on the economy. Estimating a reduced form VAR model, however, does
not allow analyzing structural shocks. Here a Cholesky decomposition will be
used to disentangle the structural shocks from their reduced form innovations.
Given the recursive structure of the Cholesky decomposition, the ordering of
the variables becomes the key aspect of the identification strategy. A short
investigation of the existing literature indicates that most studies relied on other
identification strategies. Nonetheless some assumptions can be deducted:
1. Following Christiano, Eichenbaum and Evans (1998) and Peersman
and Smets (2001) policy rate innovations have no direct effect on both
unemployment and prices. Here the sluggish reaction of the economy to
policy rate shocks is recognized.
2. In this model the assumption is that balance sheet innovations do not
have a contemporaneous effect on the federal funds rate (Peersman,
2011, Gambacorta et al., 2013, Berkman, 2012 and Shibamoto and
Tachibana, 2013). Indeed, the Federal Reserve took on a number of
non-standard monetary policies only when the federal funds rate was
stuck at the zero lower bound and could not further stimulate the
economy, not vice versa.
A last concern is the positioning of the VIX index. I found no other literature
relating to this kind of problem. Hence I will estimate two VAR models.
Afterwards, the quality of the two models will be examined. The Cholesky
ordering for each model is represented by:
Model I
Model II
!!
!"#!
!"#!
!!!
!!
!!
!"#!
!!!
!!
!"#!
35
3.3
Estimations and results
For both models the lag order is 2 and is selected by the Hannan-Quinn
information criterion. The impulse responses are displayed in Figure 6 and
Figure 7. First, the main differences between Model I and Model II are
described, subsequently they will be compared with the estimation results of
Gambacorta et al. (2013).
Figure 6: impulse responses model I (one standard deviation)
Both models generate very comparable reactions of the unemployment rate
and the federal funds rate after a one standard innovation to the balance
sheet. The two show that unconventional monetary policy successfully
compressed the unemployment rate.
36
The transmission mechanism of the VIX index and inflation, however, are
different. While Model I indicates that unconventional monetary policy leads to
a lower VIX index, the contemporaneous impact in Model II is significant
positive. The inflation in model II, on the other hand, is significant negative
after impact while this is much less prominent in Model I. In order to
demonstrate this, the accumulated responses of the inflation rate are shown in
Figure 8.
Figure 7: impulse responses model II (one standard deviation)
37
Figure 8: accumulated impulse responses of inflation for respectively model I and model II
In order to define the expected sign of the reactions I refer to the baseline VAR
model of Gambacorta et al. (2013) augmented with the policy rate. Differently
to their model I use the unemployment rate to represent the state of the
economy. This may not be an impediment as the unemployment rate typically
decreases as GDP growth increases. So, the expected sings after a balance
sheet shock are:
1. A decrease of the unemployment rate
2. A weak positive effect on inflation
3. An increase in the policy rate
4. A decrease of the VIX index at time of impact
As it turns out, Model I is most compatible with the above expectations. The
reaction of the VIX index in Model II is troublesome. Gambacorta et al. (2013)
point out that the contemporaneous impact should be negative or at least zero
while this is not the case in Model II. These findings lead to the following
conclusion: or the assumptions in Model I are legitimate, or a Cholesky
decomposition cannot properly disentangle exogenous balance sheet shocks.
Hence, it is rational to proceed with Model I. After having discussed the
identification strategy, what are the properties of the model? I find that
unconventional monetary policy was adequate in alleviating the economic
meltdown of the recent crisis. The impulse responses of the baseline model
are shown in Figure 6. The main findings can be summarized as follows:
38
•
An exogenous increase in the balance sheet of 3.8% leads to a
compression of the unemployment rate of 0.19 bp-points after 17
months. This effect, however, becomes insignificant after 28 months.
•
The Federal Reserve succeeded to temper the uncertainty on the
financial markets. The impulse response depicts a drop in the VIX index
after a balance sheet innovation.
•
Inflation reaches a peak of 0.04% after 7 months but is insignificant. An
explanation put forward by Gambacorta et al. (2013) is that the model is
estimated over a recession. Given the fact that the supply curve might
be potentially convex, a demand shock has a modest effect on inflation.
An estimated VAR model by Christiano et al. (1998) acknowledges the
similarities between conventional and unconventional monetary policy
innovations. An expansion in the federal funds rate translates into a maximum
decline in GDP after six quarters (18 months) and a permanent decline in the
price level. Yet, quantitative easing seems to be a very peculiar case, the
pattern of the transmission mechanism is similar to those of standard
operations. The degree to which the real economy reacts might be different
(Sinclair and Ellis, 2012)
3.4
Robustness Check
3.4.1 Is the model stable over time?
In this section I investigate whether the model is stable over time. Baumeister
and Benati (2010) suggested that a time varying VAR model is more
appropriate when one were to analyze the macroeconomic effects over a
longer period. Besides, Putnam (2013) pointed out that an economy might
fundamentally change when the zero lower bound is hit (supra, p. 28). Hence,
it is justifiable to change the period over which the model is estimated.
I alter the estimation period of the baseline model. Rather than including the
“Great Recession”, I estimate a VAR model without the financial crisis (20032007). The estimation output can be found in Figure 9. Although the pattern of
the transmission is similar, an exogenous rise in the balance sheet has no
39
significant effect on the economy. This might not be astonishing. Only in the
course of the last crisis the Federal Reserve employed the LSAPs as a policy
instrument. Hence, the outcome is that the parameters of the VAR model
probably change over time.
Figure 9: impulse responses model I (2003-2007) (one standard deviation)
3.4.2 A model with the Industrial Production Index
It is also worthwhile analyzing whether the model is robust for other kinds of
variables that represent the state of the economy. In my framework I replace
the unemployment rate with the industrial production index. The length span
and the ordering of the variables in the Cholesky matrix will be unchanged.
The expectation is that the industrial production should increase after a
balance sheet shock. Figure 10 displays the impulse responses. Indeed, the
40
industrial production has a positive reaction with a peak after 16 months.
Moreover, the other impulse responses are very similar as those of the
baseline model. As a result it is reasonable to conclude that the model is
robust for other variables, which grasp the state of the economy.
Figure 10: impulse responses model I with industrial production index (one standard deviation)
3.4.3 A model with the Stress Index
As a last robustness check the VIX index is replaced with the St. Louis Fed
Financial Stress Index. The Stress Index is an indicator for the amount of
stress at play in the financial markets. Again the ordering and the length span
are maintained. Figure 11 shows the estimation output in a model where the
Stress Index is used instead of the VIX index. A quick look reveals that the
properties of the model are not affected by the inclusion of the Stress Index.
41
Figure 11: impulse responses model I with Stress Index (one standard deviation)
4
Conclusion
In this dissertation I have discussed two models that embed the ability to
analyze unconventional monetary policies. Moreover, they introduce a financial
system that incorporates some rigidities. Whereas the financial intermediaries
in the CW-model face some costs in originating loans, the friction in the GKmodel consists of a financial accelerator mechanism. By introducing this new
features the models are better at reproducing the recent crisis.
A major conclusion of the CW-model is that only the purchase of assets, other
than treasuries, are effective in supporting the economy. Since treasuries and
money are perfect substitutes, agents will not alter their optimal behavior. The
42
acquisitions of MBSs on the other hand promote economic activity. The
rationale for this is that the Central Bank can act as a substitute for the
impaired financial institutions. This resembles the behavior of the Federal
Reserve during the recent crisis.
The irrelevance hypothesis does not longer hold when certain agents prefer
longer dated treasuries. When the supply of treasuries decreases, the price
will increase, leading to lower interest rates. Via the linkage of different kinds of
assets the long-term interest rate of a whole range of assets will decline.
Ultimately it is the long-term interest rate that is important for investment.
Having discussed the theoretical models I estimated a SVAR model. Herein
the structural shocks are disentangled from their reduced form shocks by
employing a Cholesky decomposition. Although the identification strategy
faces some problems and might not be an appropriate tool, the impulse
responses indicate that the Federal Reserve succeeded to lower the
unemployment rate during the recent crisis. This seems to confirm that
quantitative easing is able to support economic activity during times of turmoil.
My empirical investigation, however, does not allow analyzing whether the
positive effect stems from the acquisition of MBSs or treasuries.
5
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